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<title>Gmaps : General Maps used for Inverting Equations</title>
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<p>Type <a href="../h_definition.htm#GMAP">GMAP</a> is a collection of at most 
NV polynomials. It foes not require the INIT for DAMAPs since it is not 
connected to phase space at all.</p>
<p>GMAP main function is to solve systems of equations defined by Taylor Series. </p>

<p>For example:</p>

<p>EQ%V(1)= 2.D0*X(1)+1.D-2*X(2)**2 + 1.D-1*X(1)*X(2) -10.D0 + 0.1d0 
*(1.d0.mono.'001') <br>
EQ%V(2)= 5.D0*X(2)+1.D-2*X(2)**2 +0.1D0*SIN(X(1)*X(2)**2)-10.D0 <br>
&nbsp;</p>

<p>Here we have <b><font color="#0000FF">two</font></b> equations and <b>
<font color="#0000FF">two</font></b> unknowns. In addition we have a <b>
<font color="#0000FF">parameter</font></b> in the <b><font color="#0000FF">third 
variable</font></b>.</p>

<ul>
  <li>
<p align="left">2x<sub>1</sub>+ 10<sup>-2 </sup>x<sub>2</sub><sup>2</sup> + 10<sup>-1
</sup>x<sub>1</sub>x<sub>2 </sub>-10 + 10<sup>-1 </sup>x<sub>3</sub> = 0</p>

  </li>
  <li>
<p align="left">5x<sub>2</sub>+ 10<sup>-2 </sup>x<sub>2</sub><sup>2</sup> + 10<sup>-1
</sup>sin(x<sub>1</sub>x<sub>2</sub> ) -10&nbsp; = 0</p>

  </li>
</ul>
<p>Since there are two equations to invert, the command to allocate EQ is
<font color="#0000FF">ALLOC(EQ,2).</font></p>

<p>By default, the NV Taylor Series are allocated.</p>

<p>Solving these two equations is equivalent to the following inversion and 
evaluation:</p>

<p>&nbsp;Solution = EQ<sup>-1</sup>(0,0,x<sub>3</sub>)</p>

<p>A TPSA inversion is given by the operator .oo.</p>

<p><a href="../simple_programs/z_gmaps.f90">Click here for a program</a> solving 
the above equation. It is first solved with a parameter and then without.</p>

<p>&nbsp;</p>

<p>&nbsp;</p>

<p>&nbsp;</p>

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